\DeclareGraphicsRule{.ps}{pdf}{.pdf}{`ps2pdf -dEPSCrop -dNOSAFER #1 \noexpand\OutputFile}
\begin{document}
-\title{Lifetime Coverage Optimization Protocol \\
- in Wireless Sensor Networks} %LiCO Protocol
+%\title{Lifetime Coverage Optimization Protocol \\
+% in Wireless Sensor Networks}
+\title{Perimeter-based Coverage Optimization to Improve \\
+ Lifetime in Wireless Sensor Networks}
\author{Ali Kadhum Idrees,~\IEEEmembership{}
Karine Deschinkel,~\IEEEmembership{}
Michel Salomon,~\IEEEmembership{}
and~Rapha\"el Couturier ~\IEEEmembership{}
- \thanks{The authors are with FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comt\'e,
+ \thanks{The authors are with FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte,
Belfort, France. Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel,
michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}}
\maketitle
\begin{abstract}
-The most important problem in Wireless Sensor Networks (WSNs) is to optimize the
-use of its limited energy provision, so that it can fulfill its monitoring task
-as long as possible. Among known available approaches that can be used to
+The most important problem in a Wireless Sensor Network (WSN) is to optimize the
+use of its limited energy provision, so that it can fulfill its monitoring task
+as long as possible. Among known available approaches that can be used to
improve power management, lifetime coverage optimization provides activity
-scheduling which ensures sensing coverage while minimizing the energy cost. In
-this paper, we propose a such approach called Lifetime Coverage Optimization
-protocol (LiCO). It is a hybrid of centralized and distributed methods: the
-region of interest is first subdivided into subregions and our protocol is then
-distributed among sensor nodes in each subregion. A sensor node which runs LiCO
-protocol repeats periodically four stages: information exchange, leader
-election, optimization decision, and sensing. More precisely, the scheduling of
-nodes' activities (sleep/wake up duty cycles) is achieved in each subregion by a
-leader selected after cooperation between nodes within the same subregion. The
-novelty of approach lies essentially in the formulation of a new mathematical
-optimization model based on perimeter coverage level to schedule sensors'
-activities. Extensive simulation experiments have been performed using OMNeT++,
-the discrete event simulator, to demonstrate that LiCO is capable to offer
-longer lifetime coverage for WSNs in comparison with some other protocols.
+scheduling which ensures sensing coverage while minimizing the energy cost. In
+this paper, we propose such an approach called Perimeter-based Coverage Optimization
+protocol (PeCO). It is a hybrid of centralized and distributed methods: the
+region of interest is first subdivided into subregions and our protocol is then
+distributed among sensor nodes in each subregion.
+% A sensor node which runs LiCO protocol repeats periodically four stages:
+%information exchange, leader election, optimization decision, and sensing.
+%More precisely, the scheduling of nodes' activities (sleep/wake up duty cycles)
+%is achieved in each subregion by a leader selected after cooperation between
+%nodes within the same subregion.
+The novelty of our approach lies essentially in the formulation of a new
+mathematical optimization model based on the perimeter coverage level to schedule
+sensors' activities. Extensive simulation experiments have been performed using
+OMNeT++, the discrete event simulator, to demonstrate that PeCO can
+offer longer lifetime coverage for WSNs in comparison with some other protocols.
\end{abstract}
% Note that keywords are not normally used for peerreview papers.
\begin{IEEEkeywords}
-Wireless Sensor Networks, Area Coverage, Network lifetime, Optimization, Scheduling.
+Wireless Sensor Networks, Area Coverage, Network Lifetime, Optimization, Scheduling.
\end{IEEEkeywords}
\IEEEpeerreviewmaketitle
can send the data it collects in its environment, thanks to its sensor, to the
user by means of sink nodes. The features of a WSN made it suitable for a wide
range of application in areas such as business, environment, health, industry,
-military, and son~\cite{yick2008wireless}. Typically, a sensor node contains
+military, and so on~\cite{yick2008wireless}. Typically, a sensor node contains
three main components~\cite{anastasi2009energy}: a sensing unit able to measure
physical, chemical, or biological phenomena observed in the environment; a
processing unit which will process and store the collected measurements; a radio
communication is supplied by a power supply which is a battery. This battery has
a limited energy provision and it may be unsuitable or impossible to replace or
recharge it in most applications. Therefore it is necessary to deploy WSN with
-high density in order to increase the reliability and to exploit node redundancy
+high density in order to increase reliability and to exploit node redundancy
thanks to energy-efficient activity scheduling approaches. Indeed, the overlap
of sensing areas can be exploited to schedule alternatively some sensors in a
low power sleep mode and thus save energy. Overall, the main question that must
be answered is: how to extend the lifetime coverage of a WSN as long as possible
-while ensuring a high level of coverage? So, this last years many
+while ensuring a high level of coverage? These past few years many
energy-efficient mechanisms have been suggested to retain energy and extend the
lifetime of the WSNs~\cite{rault2014energy}.
This paper makes the following contributions.
\begin{enumerate}
-\item We devise a framework to schedule nodes to be activated alternatively such
+\item We have devised a framework to schedule nodes to be activated alternatively such
that the network lifetime is prolonged while ensuring that a certain level of
- coverage is preserved. A key idea in our framework is to exploit spatial an
- temporal subdivision. On the one hand the area of interest if divided into
- several smaller subregions and on the other hand the time line is divided into
+ coverage is preserved. A key idea in our framework is to exploit spatial and
+ temporal subdivision. On the one hand, the area of interest is divided into
+ several smaller subregions and, on the other hand, the time line is divided into
periods of equal length. In each subregion the sensor nodes will cooperatively
choose a leader which will schedule nodes' activities, and this grouping of
sensors is similar to typical cluster architecture.
-\item We propose a new mathematical optimization model. Instead of trying to
+\item We have proposed a new mathematical optimization model. Instead of trying to
cover a set of specified points/targets as in most of the methods proposed in
the literature, we formulate an integer program based on perimeter coverage of
each sensor. The model involves integer variables to capture the deviations
- between the actual level of coverage and the required level. So that an
+ between the actual level of coverage and the required level. Hence, an
optimal scheduling will be obtained by minimizing a weighted sum of these
deviations.
-\item We conducted extensive simulation experiments, using the discrete event
- simulator OMNeT++, to demonstrate the efficiency of our protocol. We compared
- our LiCO protocol to two approaches found in the literature:
+\item We have conducted extensive simulation experiments, using the discrete event
+ simulator OMNeT++, to demonstrate the efficiency of our protocol. We have compared
+ our PeCO protocol to two approaches found in the literature:
DESK~\cite{ChinhVu} and GAF~\cite{xu2001geography}, and also to our previous
work published in~\cite{Idrees2} which is based on another optimization model
for sensor scheduling.
\end{enumerate}
-%Two combined integrated energy-efficient techniques have been used by LiCO protocol in order to maximize the lifetime coverage in WSN: the first, by dividing the area of interest into several smaller subregions based on divide-and-conquer method and then one leader elected for each subregion in an independent, distributed, and simultaneous way by the cooperation among the sensor nodes within each subregion, and this similar to cluster architecture;
+%Two combined integrated energy-efficient techniques have been used by PeCO protocol in order to maximize the lifetime coverage in WSN: the first, by dividing the area of interest into several smaller subregions based on divide-and-conquer method and then one leader elected for each subregion in an independent, distributed, and simultaneous way by the cooperation among the sensor nodes within each subregion, and this similar to cluster architecture;
% the second, activity scheduling based new optimization model has been used to provide the optimal cover set that will take the mission of sensing during current period. This optimization algorithm is based on a perimeter-coverage model so as to optimize the shared perimeter among the sensors in each subregion, and this represents as a energu-efficient control topology mechanism in WSN.
The rest of the paper is organized as follows. In the next section we review
-some related work in the field. Section~\ref{sec:The LiCO Protocol Description}
-is devoted to the LiCO protocol description and Section~\ref{cp} focuses on the
+some related work in the field. Section~\ref{sec:The PeCO Protocol Description}
+is devoted to the PeCO protocol description and Section~\ref{cp} focuses on the
coverage model formulation which is used to schedule the activation of sensor
nodes. Section~\ref{sec:Simulation Results and Analysis} presents simulations
results and discusses the comparison with other approaches. Finally, concluding
-remarks are drawn and some suggestions given for future works in
+remarks are drawn and some suggestions are given for future works in
Section~\ref{sec:Conclusion and Future Works}.
% that show that our protocol outperforms others protocols.
\label{sec:Literature Review}
\noindent In this section, we summarize some related works regarding the
-coverage problem and distinguish our LiCO protocol from the works presented in
+coverage problem and distinguish our PeCO protocol from the works presented in
the literature.
The most discussed coverage problems in literature can be classified in three
categories~\cite{li2013survey} according to their respective monitoring
objective. Hence, area coverage \cite{Misra} means that every point inside a
-fixed area must be monitored, while target coverage~\cite{yang2014novel} refer
+fixed area must be monitored, while target coverage~\cite{yang2014novel} refers
to the objective of coverage for a finite number of discrete points called
targets, and barrier coverage~\cite{HeShibo}\cite{kim2013maximum} focuses on
preventing intruders from entering into the region of interest. In
-\cite{Deng2012} authors transform the area coverage problem to the target
+\cite{Deng2012} authors transform the area coverage problem into the target
coverage one taking into account the intersection points among disks of sensors
nodes or between disk of sensor nodes and boundaries. In
\cite{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of
sensors are sufficiently covered it will be the case for the whole area. They
provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of
each sensor, where $d$ denotes the maximum number of sensors that are
-neighboring to a sensor and $n$ is the total number of sensors in the
-network. {\it In LiCO protocol, instead of determining the level of coverage of
+neighbors to a sensor and $n$ is the total number of sensors in the
+network. {\it In PeCO protocol, instead of determining the level of coverage of
a set of discrete points, our optimization model is based on checking the
perimeter-coverage of each sensor to activate a minimal number of sensors.}
activated in succession to achieve the desired network lifetime. Vu
\cite{chin2007}, Padmatvathy {\em et al.}~\cite{pc10}, propose algorithms
working in a periodic fashion where a cover set is computed at the beginning of
-each period. {\it Motivated by these works, LiCO protocol works in periods,
+each period. {\it Motivated by these works, PeCO protocol works in periods,
where each period contains a preliminary phase for information exchange and
decisions, followed by a sensing phase where one cover set is in charge of the
sensing task.}
-Various centralized and distributed approaches, or even a mixing of these two
+Various centralized and distributed approaches, or even a mixing of these two
concepts, have been proposed to extend the network lifetime. In distributed
-algorithms~\cite{yangnovel,ChinhVu,qu2013distributed} each sensors decides of
-its own activity scheduling after an information exchange with its neighbors.
-The main interest of a such approach is to avoid long range communications and
-thus to reduce the energy dedicated to the communications. Unfortunately, since
-each node has only information on its immediate neighbors (usually the one-hop
-ones) it may take a bad decision leading to a global suboptimal solution.
-Conversely, centralized
-algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high} always
+algorithms~\cite{yangnovel,ChinhVu,qu2013distributed} each sensor decides of its
+own activity scheduling after an information exchange with its neighbors. The
+main interest of such an approach is to avoid long range communications and thus
+to reduce the energy dedicated to the communications. Unfortunately, since each
+node has only information on its immediate neighbors (usually the one-hop ones)
+it may make a bad decision leading to a global suboptimal solution. Conversely,
+centralized
+algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high} always
provide nearly or close to optimal solution since the algorithm has a global
view of the whole network. The disadvantage of a centralized method is obviously
-its high cost in communications needed to transmit to a single node, the base
-station which will globally schedule nodes' activities, data from all the other
-sensor nodes in the area. The price in communications can be very huge since
-long range communications will be needed. In fact the larger the WNS, the higher
-the communication and thus energy cost. {\it In order to be suitable for
- large-scale networks, in the LiCO protocol the area of interest is divided
- into several smaller subregions, and in each one, a node called the leader is
- in charge for selecting the active sensors for the current period. Thus our
- protocol is scalable and a globally distributed method, whereas it is
- centralized in each subregion.}
-
-Various coverage scheduling algorithms have been developed this last years.
+its high cost in communications needed to transmit to a single node, the base
+station which will globally schedule nodes' activities, data from all the other
+sensor nodes in the area. The price in communications can be huge since
+long range communications will be needed. In fact the larger the WNS is, the
+higher the communication and thus the energy cost are. {\it In order to be
+ suitable for large-scale networks, in the PeCO protocol, the area of interest
+ is divided into several smaller subregions, and in each one, a node called the
+ leader is in charge of selecting the active sensors for the current
+ period. Thus our protocol is scalable and is a globally distributed method,
+ whereas it is centralized in each subregion.}
+
+Various coverage scheduling algorithms have been developed these past few years.
Many of them, dealing with the maximization of the number of cover sets, are
heuristics. These heuristics involve the construction of a cover set by
including in priority the sensor nodes which cover critical targets, that is to
energy constraints. Column generation techniques, well-known and widely
practiced techniques for solving linear programs with too many variables, have
also been
-used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In LiCO
+used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In the PeCO
protocol, each leader, in charge of a subregion, solves an integer program
which has a twofold objective: minimize the overcoverage and the undercoverage
of the perimeter of each sensor.}
%\uppercase{\textbf{shortcomings}}. In spite of many energy-efficient protocols for maintaining the coverage and improving the network lifetime in WSNs were proposed, non of them ensure the coverage for the sensing field with optimal minimum number of active sensor nodes, and for a long time as possible. For example, in a full centralized algorithms, an optimal solutions can be given by using optimization approaches, but in the same time, a high energy is consumed for the execution time of the algorithm and the communications among the sensors in the sensing field, so, the full centralized approaches are not good candidate to use it especially in large WSNs. Whilst, a full distributed algorithms can not give optimal solutions because this algorithms use only local information of the neighboring sensors, but in the same time, the energy consumption during the communications and executing the algorithm is highly lower. Whatever the case, this would result in a shorter lifetime coverage in WSNs.
-%\uppercase{\textbf{Our Protocol}}. In this paper, a Lifetime Coverage Optimization Protocol, called (LiCO) in WSNs is suggested. The sensing field is divided into smaller subregions by means of divide-and-conquer method, and a LiCO protocol is distributed in each sensor in the subregion. The network lifetime in each subregion is divided into periods, each period includes 4 stages: Information Exchange, Leader election, decision based activity scheduling optimization, and sensing. The leaders are elected in an independent, asynchronous, and distributed way in all the subregions of the WSN. After that, energy-efficient activity scheduling mechanism based new optimization model is performed by each leader in the subregions. This optimization model is based on the perimeter coverage model in order to producing the optimal cover set of active sensors, which are taken the responsibility of sensing during the current period. LiCO protocol merges between two energy efficient mechanisms, which are used the main advantages of the centralized and distributed approaches and avoids the most of their disadvantages.
+%\uppercase{\textbf{Our Protocol}}. In this paper, a Lifetime Coverage Optimization Protocol, called (PeCO) in WSNs is suggested. The sensing field is divided into smaller subregions by means of divide-and-conquer method, and a PeCO protocol is distributed in each sensor in the subregion. The network lifetime in each subregion is divided into periods, each period includes 4 stages: Information Exchange, Leader election, decision based activity scheduling optimization, and sensing. The leaders are elected in an independent, asynchronous, and distributed way in all the subregions of the WSN. After that, energy-efficient activity scheduling mechanism based new optimization model is performed by each leader in the subregions. This optimization model is based on the perimeter coverage model in order to producing the optimal cover set of active sensors, which are taken the responsibility of sensing during the current period. PeCO protocol merges between two energy efficient mechanisms, which are used the main advantages of the centralized and distributed approaches and avoids the most of their disadvantages.
-\section{ The LiCO Protocol Description}
-\label{sec:The LiCO Protocol Description}
+\section{ The PeCO Protocol Description}
+\label{sec:The PeCO Protocol Description}
-\noindent In this section, we describe in details our Lifetime Coverage
+\noindent In this section, we describe in details our Perimeter-based Coverage
Optimization protocol. First we present the assumptions we made and the models
we considered (in particular the perimeter coverage one), second we describe the
background idea of our protocol, and third we give the outline of the algorithm
deployed in high density to ensure initially a high coverage ratio of the area
of interest. We assume that all the sensor nodes are homogeneous in terms of
communication, sensing, and processing capabilities and heterogeneous from
-energy provision point of view. The location information is available to a
+the energy provision point of view. The location information is available to a
sensor node either through hardware such as embedded GPS or location discovery
algorithms. We assume that each sensor node can directly transmit its
measurements to a mobile sink node. For example, a sink can be an unmanned
within a disk centered at a sensor with a radius equal to the sensing range are
said to be covered by this sensor. We also assume that the communication range
$R_c$ satisfies $R_c \geq 2 \cdot R_s$. In fact, Zhang and Zhou~\cite{Zhang05}
-proved that if the transmission range fulfills the previous hypothesis, a
+proved that if the transmission range fulfills the previous hypothesis, the
complete coverage of a convex area implies connectivity among active nodes.
-\indent LiCO protocol uses the same perimeter-coverage model than Huang and
+The PeCO protocol uses the same perimeter-coverage model as Huang and
Tseng in~\cite{huang2005coverage}. It can be expressed as follows: a sensor is
said to be perimeter covered if all the points on its perimeter are covered by
at least one sensor other than itself. They proved that a network area is
-$k$-covered if and only if each sensor in the network is $k$-perimeter-covered.
+$k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).
%According to this model, we named the intersections among the sensor nodes in the sensing field as intersection points. Instead of working with the coverage area, we consider for each sensor a set of intersection points which are determined by using perimeter-coverage model.
Figure~\ref{pcm2sensors}(a) shows the coverage of sensor node~$0$. On this
figure, we can see that sensor~$0$ has nine neighbors and we have reported on
its perimeter (the perimeter of the disk covered by the sensor) for each
-neighbor the two points resulting from intersection of the two sensing
+neighbor the two points resulting from the intersection of the two sensing
areas. These points are denoted for neighbor~$i$ by $iL$ and $iR$, respectively
-for left and right from neighbor point of view. The resulting couples of
+for left and right from a neighboing point of view. The resulting couples of
intersection points subdivide the perimeter of sensor~$0$ into portions called
arcs.
\begin{figure}[ht!]
\centering
\begin{tabular}{@{}cr@{}}
- \includegraphics[width=75mm]{pcm.jpg} & \raisebox{3.25cm}{(a)}
- \\ \includegraphics[width=75mm]{twosensors.jpg} & \raisebox{2.75cm}{(b)}
+ \includegraphics[width=75mm]{pcm.jpg} & \raisebox{3.25cm}{(a)} \\
+ \includegraphics[width=75mm]{twosensors.jpg} & \raisebox{2.75cm}{(b)}
\end{tabular}
\caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of
$u$'s perimeter covered by $v$.}
Figure~\ref{pcm2sensors}(b) describes the geometric information used to find the
locations of the left and right points of an arc on the perimeter of a sensor
-node~$u$ covered by a sensor node~$v$. Node~$s$ is supposed to be located on the
+node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the
west side of sensor~$u$, with the following respective coordinates in the
sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can
compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert
u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is
-obtained through the formula $\alpha = arccos \left(\dfrac{Dist(u,v)}{2R_s}
-\right)$. So, the arc on the perimeter of node~$u$ defined by the angular
-interval $[\pi - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor
-node $v$.
+obtained through the formula: $$\alpha = \arccos \left(\dfrac{Dist(u,v)}{2R_s}
+\right).$$ The arc on the perimeter of~$u$ defined by the angular interval $[\pi
+ - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$.
Every couple of intersection points is placed on the angular interval $[0,2\pi]$
in a counterclockwise manner, leading to a partitioning of the interval.
Figure~\ref{pcm2sensors}(a) illustrates the arcs for the nine neighbors of
-sensor $0$ and figure~\ref{expcm} gives the position of the corresponding arcs
+sensor $0$ and Figure~\ref{expcm} gives the position of the corresponding arcs
in the interval $[0,2\pi]$. More precisely, we can see that the points are
ordered according to the measures of the angles defined by their respective
positions. The intersection points are then visited one after another, starting
-from first intersection point after point~zero, and the maximum level of
+from the first intersection point after point~zero, and the maximum level of
coverage is determined for each interval defined by two successive points. The
maximum level of coverage is equal to the number of overlapping arcs. For
-example, between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$
-(the value is highlighted in yellow at the bottom of figure~\ref{expcm}), which
-means that at most 2~neighbors can cover the perimeter in addition to node $0$.
+example,
+between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$
+(the value is highlighted in yellow at the bottom of Figure~\ref{expcm}), which
+means that at most 2~neighbors can cover the perimeter in addition to node $0$.
Table~\ref{my-label} summarizes for each coverage interval the maximum level of
coverage and the sensor nodes covering the perimeter. The example discussed
above is thus given by the sixth line of the table.
%The points reported on the line segment $[0,2\pi]$ separates it in intervals as shown in figure~\ref{expcm}. For example, for each neighboring sensor of sensor 0, place the points $\alpha^ 1_L$, $\alpha^ 1_R$, $\alpha^ 2_L$, $\alpha^ 2_R$, $\alpha^ 3_L$, $\alpha^ 3_R$, $\alpha^ 4_L$, $\alpha^ 4_R$, $\alpha^ 5_L$, $\alpha^ 5_R$, $\alpha^ 6_L$, $\alpha^ 6_R$, $\alpha^ 7_L$, $\alpha^ 7_R$, $\alpha^ 8_L$, $\alpha^ 8_R$, $\alpha^ 9_L$, and $\alpha^ 9_R$; on the line segment $[0,2\pi]$, and then sort all these points in an ascending order into a list. Traverse the line segment $[0,2\pi]$ by visiting each point in the sorted list from left to right and determine the coverage level of each interval of the sensor 0 (see figure \ref{expcm}). For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. Table~\ref{my-label} summarizes the level of coverage for each interval and the sensors involved in for sensor node 0 in figure~\ref{pcm2sensors}(a).
% to determine the level of the perimeter coverage for each left and right point of a segment.
-\begin{figure*}[ht!]
+\begin{figure*}[t!]
\centering
-\includegraphics[width=137.5mm]{expcm.pdf}
+\includegraphics[width=127.5mm]{expcm2.jpg}
\caption{Maximum coverage levels for perimeter of sensor node $0$.}
\label{expcm}
\end{figure*}
\fi
- \begin{table}[h]
+ \begin{table}[h!]
\caption{Coverage intervals and contributing sensors for sensor node 0.}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
-\begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\ level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in interval coverage\end{tabular}} \\ \hline
+\begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\ level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in coverage interval\end{tabular}} \\ \hline
0.0291 & 1L & 2L & 4 & 0 & 1 & 3 & 4 & \\ \hline
0.104 & 2L & 3R & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline
0.3168 & 3R & 4R & 4 & 0 & 1 & 4 & 2 & \\ \hline
\end{table}
-%The optimization algorithm that used by LiCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1.
+%The optimization algorithm that used by PeCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1.
-In LiCO protocol, scheduling of sensor nodes' activities is formulated with an
+In the PeCO protocol, the scheduling of the sensor nodes' activities is formulated with an
integer program based on coverage intervals. The formulation of the coverage
optimization problem is detailed in~section~\ref{cp}. Note that when a sensor
node has a part of its sensing range outside the WSN sensing field, as in
-figure~\ref{ex4pcm}, the maximum coverage level for this arc is set to $\infty$
+Figure~\ref{ex4pcm}, the maximum coverage level for this arc is set to $\infty$
and the corresponding interval will not be taken into account by the
optimization algorithm.
-\begin{figure}[t!]
+\begin{figure}[h!]
\centering
\includegraphics[width=62.5mm]{ex4pcm.jpg}
\caption{Sensing range outside the WSN's area of interest.}
our protocol will be executed in a distributed way in each subregion
simultaneously to schedule nodes' activities for one sensing period.
-As shown in figure~\ref{fig2}, node activity scheduling is produced by our
+As shown in Figure~\ref{fig2}, node activity scheduling is produced by our
protocol in a periodic manner. Each period is divided into 4 stages: Information
(INFO) Exchange, Leader Election, Decision (the result of an optimization
problem), and Sensing. For each period there is exactly one set cover
responsible for the sensing task. Protocols based on a periodic scheme, like
-LiCO, are more robust against an unexpected node failure. On the one hand, if
-node failure is discovered before taking the decision, the corresponding sensor
-node will not be considered by the optimization algorithm, and, on the other
+PeCO, are more robust against an unexpected node failure. On the one hand, if
+a node failure is discovered before taking the decision, the corresponding sensor
+node will not be considered by the optimization algorithm. On the other
hand, if the sensor failure happens after the decision, the sensing task of the
network will be temporarily affected: only during the period of sensing until a
new period starts, since a new set cover will take charge of the sensing task in
\begin{figure}[t!]
\centering
\includegraphics[width=80mm]{Model.pdf}
-\caption{LiCO protocol}
+\caption{PeCO protocol.}
\label{fig2}
\end{figure}
-We define two types of packets to be used by LiCO protocol:
+We define two types of packets to be used by PeCO protocol:
%\begin{enumerate}[(a)]
\begin{itemize}
\item INFO packet: sent by each sensor node to all the nodes inside a same
determine the activities scheduling;
\item ACTIVE: node is sensing;
\item SLEEP: node is turned off;
-\item COMMUNICATION: transmits or recevives packets.
+\item COMMUNICATION: transmits or receives packets.
\end{itemize}
%\end{enumerate}
%Below, we describe each phase in more details.
-\subsection{LiCO Protocol Algorithm}
+\subsection{PeCO Protocol Algorithm}
\noindent The pseudocode implementing the protocol on a node is given below.
-More precisely, Algorithm~\ref{alg:LiCO} gives a brief description of the
+More precisely, Algorithm~\ref{alg:PeCO} gives a brief description of the
protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
\begin{algorithm}[h!]
}
\emph{$s_k.status$ = COMMUNICATION}\;
- \emph{Send $ActiveSleep()$ to each node $l$ in subregion} \;
+ \emph{Send $ActiveSleep()$ to each node $l$ in subregion}\;
\emph{Update $RE_k $}\;
}
\Else{
}
}
\Else { Exclude $s_k$ from entering in the current sensing stage}
-\caption{LiCO($s_k$)}
-\label{alg:LiCO}
+\caption{PeCO($s_k$)}
+\label{alg:PeCO}
\end{algorithm}
-In this algorithm, K.CurrentSize and K.PreviousSize refer to the current size
-and the previous size of the subnetwork in the subregion respectively. That
-means the number of sensor nodes which are still alive. Initially, the sensor
-node checks its remaining energy $RE_k$, which must be greater than a threshold
-$E_{th}$ in order to participate in the current period. Each sensor node
-determines its position and its subregion using an embedded GPS or a location
-discovery algorithm. After that, all the sensors collect position coordinates,
-remaining energy, sensor node ID, and the number of its one-hop live neighbors
-during the information exchange. The sensors inside a same region cooperate to
-elect a leader. The selection criteria for the leader, in order of priority,
-are: larger number of neighbors, larger remaining energy, and then in case of
-equality, larger index. Once chosen, the leader collects information to
-formulate and solve the integer program which allows to construct the set of
-active sensors in the sensing stage.
-
-%After the cooperation among the sensor nodes in the same subregion, the leader will be elected in distributed way, where each sensor node and based on it's information decide who is the leader. The selection criteria for the leader in order of priority are: larger number of neighbors, larger remaining energy, and then in case of equality, larger index. Thereafter, if the sensor node is leader, it will execute the perimeter-coverage model for each sensor in the subregion in order to determine the segment points which would be used in the next stage by the optimization algorithm of the LiCO protocol. Every sensor node is selected as a leader, it is executed the perimeter coverage model only one time during it's life in the network.
+In this algorithm, K.CurrentSize and K.PreviousSize respectively represent the
+current number and the previous number of living nodes in the subnetwork of the
+subregion. Initially, the sensor node checks its remaining energy $RE_k$, which
+must be greater than a threshold $E_{th}$ in order to participate in the current
+period. Each sensor node determines its position and its subregion using an
+embedded GPS or a location discovery algorithm. After that, all the sensors
+collect position coordinates, remaining energy, sensor node ID, and the number
+of their one-hop live neighbors during the information exchange. The sensors
+inside a same region cooperate to elect a leader. The selection criteria for the
+leader, in order of priority, are: larger numbers of neighbors, larger remaining
+energy, and then in case of equality, larger index. Once chosen, the leader
+collects information to formulate and solve the integer program which allows to
+construct the set of active sensors in the sensing stage.
+
+%After the cooperation among the sensor nodes in the same subregion, the leader will be elected in distributed way, where each sensor node and based on it's information decide who is the leader. The selection criteria for the leader in order of priority are: larger number of neighbors, larger remaining energy, and then in case of equality, larger index. Thereafter, if the sensor node is leader, it will execute the perimeter-coverage model for each sensor in the subregion in order to determine the segment points which would be used in the next stage by the optimization algorithm of the PeCO protocol. Every sensor node is selected as a leader, it is executed the perimeter coverage model only one time during it's life in the network.
% The leader has the responsibility of applying the integer program algorithm (see section~\ref{cp}), which provides a set of sensors planned to be active in the sensing stage. As leader, it will send an Active-Sleep packet to each sensor in the same subregion to inform it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing stage.
-\section{Lifetime Coverage problem formulation}
+\section{Perimeter-based Coverage Problem Formulation}
\label{cp}
\noindent In this section, the coverage model is mathematically formulated. We
-start with a description of the notations that will be used throughout the
+start with a description of the notations that will be used throughout the
section.
First, we have the following sets:
\end{itemize}
$I_j$ refers to the set of coverage intervals which have been defined according
to the method introduced in subsection~\ref{CI}. For a coverage interval $i$,
-let $a^j_{ik}$ denote the indicator function of whether sensor~$k$ is involved
+let $a^j_{ik}$ denotes the indicator function of whether sensor~$k$ is involved
in coverage interval~$i$ of sensor~$j$, that is:
\begin{equation}
a^j_{ik} = \left \{
lifetime, the objective is to activate a minimal number of sensors in each
period to ensure the desired coverage level. As the number of alive sensors
decreases, it becomes impossible to reach the desired level of coverage for all
-coverage intervals. Therefore we uses variables $M^j_i$ and $V^j_i$ as a measure
+coverage intervals. Therefore we use variables $M^j_i$ and $V^j_i$ as a measure
of the deviation between the desired number of active sensors in a coverage
interval and the effective number. And we try to minimize these deviations,
first to force the activation of a minimal number of sensors to ensure the
$\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the
relative importance of satisfying the associated level of coverage. For example,
weights associated with coverage intervals of a specified part of a region may
-be given a relatively larger magnitude than weights associated with another
+be given by a relatively larger magnitude than weights associated with another
region. This kind of integer program is inspired from the model developed for
-brachytherapy treatment planning for optimizing dose distribution
+brachytherapy treatment planning for optimizing dose distribution
\cite{0031-9155-44-1-012}. The integer program must be solved by the leader in
each subregion at the beginning of each sensing phase, whenever the environment
has changed (new leader, death of some sensors). Note that the number of
each time 25~randomly generated networks. The nodes are deployed on a field of
interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
high coverage ratio. Each node has an initial energy level, in Joules, which is
-randomly drawn in the interval $[500-700]$. If it's energy provision reaches a
+randomly drawn in the interval $[500-700]$. If its energy provision reaches a
value below the threshold $E_{th}=36$~Joules, the minimum energy needed for a
node to stay active during one period, it will no more participate in the
coverage task. This value corresponds to the energy needed by the sensing phase,
be active during at most 20 periods.
The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good
-network coverage and a longer WSN lifetime. We have given a higher priority for
+network coverage and a longer WSN lifetime. We have given a higher priority to
the undercoverage (by setting the $\alpha^j_i$ with a larger value than
-$\beta^j_i$) so as to prevent the non-coverage for the interval i of the sensor
-j. On the other hand, we have given a little bit lower value for $\beta^j_i$ so
-as to minimize the number of active sensor nodes which contribute in covering
-the interval.
+$\beta^j_i$) so as to prevent the non-coverage for the interval~$i$ of the
+sensor~$j$. On the other hand, we have assigned to
+$\beta^j_i$ a value which is slightly lower so as to minimize the number of active sensor nodes which contribute
+in covering the interval.
We introduce the following performance metrics to evaluate the efficiency of our
approach.
$Lifetime_{50}$ denote, respectively, the amount of time during which is
guaranteed a level of coverage greater than $95\%$ and $50\%$. The WSN can
fulfill the expected monitoring task until all its nodes have depleted their
- energy or if the network is not more connected. This last condition is crucial
+ energy or if the network is no more connected. This last condition is crucial
because without network connectivity a sensor may not be able to send to a
base station an event it has sensed.
\item {\bf Coverage Ratio (CR)} : it measures how well the WSN is able to
points in the sensing field. In our simulations we have set a layout of
$N~=~51~\times~26~=~1326$~grid points.
\item {\bf Active Sensors Ratio (ASR)}: a major objective of our protocol is to
- activate nodes as few as possible, in order to minimize the communication
+ activate as few nodes as possible, in order to minimize the communication
overhead and maximize the WSN lifetime. The active sensors ratio is defined as
follows:
\begin{equation*}
\scriptsize
- \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r|$}}{\mbox{$|S|$}} \times 100
+ \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|S|$}} \times 100
\end{equation*}
where $|A_r^p|$ is the number of active sensors in the subregion $r$ in the
current sensing period~$p$, $|S|$ is the number of sensors in the network, and
\subsection{Simulation Results}
In order to assess and analyze the performance of our protocol we have
-implemented LiCO protocol in OMNeT++~\cite{varga} simulator. Besides LiCO, two
+implemented PeCO protocol in OMNeT++~\cite{varga} simulator. Besides PeCO, two
other protocols, described in the next paragraph, will be evaluated for
-comparison purposes. The simulations were run on a laptop DELL with an Intel
+comparison purposes. The simulations were run on a DELL laptop with an Intel
Core~i3~2370~M (2.4~GHz) processor (2 cores) whose MIPS (Million Instructions
Per Second) rate is equal to 35330. To be consistent with the use of a sensor
node based on Atmels AVR ATmega103L microcontroller (6~MHz) having a MIPS rate
optimization solver GLPK (GNU linear Programming Kit available in the public
domain) \cite{glpk} through a Branch-and-Bound method.
-As said previously, the LiCO is compared with three other approaches. The first
+As said previously, the PeCO is compared to three other approaches. The first
one, called DESK, is a fully distributed coverage algorithm proposed by
\cite{ChinhVu}. The second one, called GAF~\cite{xu2001geography}, consists in
dividing the monitoring area into fixed squares. Then, during the decision
phase, in each square, one sensor is chosen to remain active during the sensing
phase. The last one, the DiLCO protocol~\cite{Idrees2}, is an improved version
of a research work we presented in~\cite{idrees2014coverage}. Let us notice that
-LiCO and DiLCO protocols are based on the same framework. In particular, the
-choice for the simulations of a partitioning in 16~subregions was chosen because
-it corresponds to the configuration producing the better results for DiLCO. The
+PeCO and DiLCO protocols are based on the same framework. In particular, the
+choice for the simulations of a partitioning in 16~subregions was made because
+it corresponds to the configuration producing the best results for DiLCO. The
protocols are distinguished from one another by the formulation of the integer
program providing the set of sensors which have to be activated in each sensing
phase. DiLCO protocol tries to satisfy the coverage of a set of primary points,
-whereas LICO protocol objectif is to reach a desired level of coverage for each
+whereas the PeCO protocol objective is to reach a desired level of coverage for each
sensor perimeter. In our experimentations, we chose a level of coverage equal to
one ($l=1$).
\subsubsection{\bf Coverage Ratio}
Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes
-obtained with the four protocols. DESK, GAF, and DiLCO provide a little better
-coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, against 98.76\%
-produced by LiCO for the first periods. This is due to the fact that at the
-beginning DiLCO protocol puts in sleep status more redundant sensors (which
+obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better
+coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the 98.76\%
+produced by PeCO for the first periods. This is due to the fact that at the
+beginning the DiLCO protocol puts to sleep status more redundant sensors (which
slightly decreases the coverage ratio), while the three other protocols activate
more sensor nodes. Later, when the number of periods is beyond~70, it clearly
-appears that LiCO provides a better coverage ratio and keeps a coverage ratio
+appears that PeCO provides a better coverage ratio and keeps a coverage ratio
greater than 50\% for longer periods (15 more compared to DiLCO, 40 more
-compared to DESK). The energy saved by LiCO in the early periods allows later a
+compared to DESK). The energy saved by PeCO in the early periods allows later a
substantial increase of the coverage performance.
\parskip 0pt
\label{fig333}
\end{figure}
-%When the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to LiCO protocol. The coverage ratio of LiCO protocol is better than other approaches from the period 64.
+%When the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to PeCO protocol. The coverage ratio of PeCO protocol is better than other approaches from the period 64.
-%because the optimization algorithm used by LiCO has been optimized the lifetime coverage based on the perimeter coverage model, so it provided acceptable coverage for a larger number of periods and prolonging the network lifetime based on the perimeter of the sensor nodes in each subregion of WSN. Although some nodes are dead, sensor activity scheduling based optimization of LiCO selected another nodes to ensure the coverage of the area of interest. i.e. DiLCO-16 showed a good coverage in the beginning then LiCO, when the number of periods increases, the coverage ratio decreases due to died sensor nodes. Meanwhile, thanks to sensor activity scheduling based new optimization model, which is used by LiCO protocol to ensure a longer lifetime coverage in comparison with other approaches.
+%because the optimization algorithm used by PeCO has been optimized the lifetime coverage based on the perimeter coverage model, so it provided acceptable coverage for a larger number of periods and prolonging the network lifetime based on the perimeter of the sensor nodes in each subregion of WSN. Although some nodes are dead, sensor activity scheduling based optimization of PeCO selected another nodes to ensure the coverage of the area of interest. i.e. DiLCO-16 showed a good coverage in the beginning then PeCO, when the number of periods increases, the coverage ratio decreases due to died sensor nodes. Meanwhile, thanks to sensor activity scheduling based new optimization model, which is used by PeCO protocol to ensure a longer lifetime coverage in comparison with other approaches.
\subsubsection{\bf Active Sensors Ratio}
Having the less active sensor nodes in each period is essential to minimize the
-energy consumption and so maximize the network lifetime. Figure~\ref{fig444}
+energy consumption and thus to maximize the network lifetime. Figure~\ref{fig444}
shows the average active nodes ratio for 200 deployed nodes. We observe that
DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen
-rounds and DiLCO and LiCO protocols compete perfectly with only 17.92 \% and
+rounds and DiLCO and PeCO protocols compete perfectly with only 17.92 \% and
20.16 \% active nodes during the same time interval. As the number of periods
-increases, LiCO protocol has a lower number of active nodes in comparison with
+increases, PeCO protocol has a lower number of active nodes in comparison with
the three other approaches, while keeping a greater coverage ratio as shown in
-figure \ref{fig333}.
+Figure \ref{fig333}.
\begin{figure}[h!]
\centering
\subsubsection{\bf Energy Consumption}
-We study the effect of the energy consumed by the WSN during the communication,
+We studied the effect of the energy consumed by the WSN during the communication,
computation, listening, active, and sleep status for different network densities
-and compare it for the fours approaches. Figures~\ref{fig3EC}(a) and (b)
+and compared it for the four approaches. Figures~\ref{fig3EC}(a) and (b)
illustrate the energy consumption for different network sizes and for
-$Lifetime95$ and $Lifetime50$. The results show that our LiCO protocol is the
+$Lifetime95$ and $Lifetime50$. The results show that our PeCO protocol is the
most competitive from the energy consumption point of view. As shown in both
-figures, LiCO consumes much less energy than the three other methods. One might
+figures, PeCO consumes much less energy than the three other methods. One might
think that the resolution of the integer program is too costly in energy, but
the results show that it is very beneficial to lose a bit of time in the
selection of sensors to activate. Indeed the optimization program allows to
\label{fig3EC}
\end{figure}
-%The optimization algorithm, which used by LiCO protocol, was improved the lifetime coverage efficiently based on the perimeter coverage model.
+%The optimization algorithm, which used by PeCO protocol, was improved the lifetime coverage efficiently based on the perimeter coverage model.
%The other approaches have a high energy consumption due to activating a larger number of sensors. In fact, a distributed method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks.
\subsubsection{\bf Network Lifetime}
-We observe the superiority of LiCO and DiLCO protocols in comparison against the
-two other approaches in prolonging the network WSN. In figures~\ref{fig3LT}(a)
-and (b), $Lifetime95$ and $Lifetime50$ are shown for different network sizes.
-As highlighted by these figures, the lifetime increases with the size of the
-network, and it is clearly the larger for DiLCO and LiCO protocols. For
-instance, for a network of 300 sensors and coverage ratio greater than 50\%, we
-can see on figure~\ref{fig3LT}(b) that the lifetime is about two times longer
-with LiCO compared to DESK protocol. The performance difference is more obvious
-in figure~\ref{fig3LT}(b) than in figure~\ref{fig3LT}(a) because the gain
-induced by our protocols increases with the time, and the lifetime with a
-coverage of 50\% is far more longer than with 95\%.
+We observe the superiority of PeCO and DiLCO protocols in comparison with the
+two other approaches in prolonging the network lifetime. In
+Figures~\ref{fig3LT}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for
+different network sizes. As highlighted by these figures, the lifetime
+increases with the size of the network, and it is clearly largest for DiLCO
+and PeCO protocols. For instance, for a network of 300~sensors and coverage
+ratio greater than 50\%, we can see on Figure~\ref{fig3LT}(b) that the lifetime
+is about twice longer with PeCO compared to DESK protocol. The performance
+difference is more obvious in Figure~\ref{fig3LT}(b) than in
+Figure~\ref{fig3LT}(a) because the gain induced by our protocols increases with
+ time, and the lifetime with a coverage of 50\% is far longer than with
+95\%.
\begin{figure}[h!]
\centering
\label{fig3LT}
\end{figure}
-%By choosing the best suited nodes, for each period, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next rounds, LiCO protocol efficiently prolonged the network lifetime especially for a coverage ratio greater than $50 \%$, whilst it stayed very near to DiLCO-16 protocol for $95 \%$.
+%By choosing the best suited nodes, for each period, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next rounds, PeCO protocol efficiently prolonged the network lifetime especially for a coverage ratio greater than $50 \%$, whilst it stayed very near to DiLCO-16 protocol for $95 \%$.
Figure~\ref{figLTALL} compares the lifetime coverage of our protocols for
different coverage ratios. We denote by Protocol/50, Protocol/80, Protocol/85,
Protocol/90, and Protocol/95 the amount of time during which the network can
satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$
-respectively, where Protocol is DiLCO or LiCO. Indeed there are applications
-that do not require a 100\% coverage of the area to be monitored. LiCO might be
+respectively, where the term Protocol refers to DiLCO or PeCO. Indeed there are applications
+that do not require a 100\% coverage of the area to be monitored. PeCO might be
an interesting method since it achieves a good balance between a high level
-coverage ratio and network lifetime. LiCO always outperforms DiLCO for the three
+coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three
lower coverage ratios, moreover the improvements grow with the network
-size. DiLCO is better for coverage ratios near 100\%, but LiCO is not so bad for
-the smallest network sizes.
+size. DiLCO is better for coverage ratios near 100\%, but in that case PeCO is
+not ineffective for the smallest network sizes.
\begin{figure}[h!]
\centering \includegraphics[scale=0.5]{R/LTa.eps}
\label{figLTALL}
\end{figure}
-%Comparison shows that LiCO protocol, which are used distributed optimization over the subregions, is the more relevance one for most coverage ratios and WSN sizes because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. LiCO protocol gave acceptable coverage ratio for a larger number of periods using new optimization algorithm that based on a perimeter coverage model. It also means that distributing the algorithm in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
+%Comparison shows that PeCO protocol, which are used distributed optimization over the subregions, is the more relevance one for most coverage ratios and WSN sizes because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. PeCO protocol gave acceptable coverage ratio for a larger number of periods using new optimization algorithm that based on a perimeter coverage model. It also means that distributing the algorithm in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
\section{Conclusion and Future Works}
\label{sec:Conclusion and Future Works}
-In this paper we have studied the problem of lifetime coverage optimization in
-WSNs. We designed a new protocol, called Lifetime Coverage Optimization, which
-schedules node' activities (wake up and sleep stages) with the objective of
+In this paper we have studied the problem of Perimeter-based Coverage Optimization in
+WSNs. We have designed a new protocol, called Perimeter-based Coverage Optimization, which
+schedules nodes' activities (wake up and sleep stages) with the objective of
maintaining a good coverage ratio while maximizing the network lifetime. This
protocol is applied in a distributed way in regular subregions obtained after
partitioning the area of interest in a preliminary step. It works in periods and
sensors based on their perimeter coverage level, instead of using a set of
targets/points to be covered.
-%To cope with this problem, the area of interest is divided into a smaller subregions using divide-and-conquer method, and then a LiCO protocol for optimizing the lifetime coverage in each subregion. LiCO protocol combines two efficient techniques: network
+%To cope with this problem, the area of interest is divided into a smaller subregions using divide-and-conquer method, and then a PeCO protocol for optimizing the lifetime coverage in each subregion. PeCO protocol combines two efficient techniques: network
%leader election, which executes the perimeter coverage model (only one time), the optimization algorithm, and sending the schedule produced by the optimization algorithm to other nodes in the subregion ; the second, sensor activity scheduling based optimization in which a new lifetime coverage optimization model is proposed. The main challenges include how to select the most efficient leader in each subregion and the best schedule of sensor nodes that will optimize the network lifetime coverage
%in the subregion.
%The network lifetime coverage in each subregion is divided into
%periods, each period consists of four stages: (i) Information Exchange,
%(ii) Leader Election, (iii) a Decision based new optimization model in order to
%select the nodes remaining active for the last stage, and (iv) Sensing.
-We carried out several simulations to evaluate the proposed protocol. The
-simulation results show that LiCO is more energy-efficient than other
+We have carried out several simulations to evaluate the proposed protocol. The
+simulation results show that PeCO is more energy-efficient than other
approaches, with respect to lifetime, coverage ratio, active sensors ratio, and
energy consumption.
%Indeed, when dealing with large and dense WSNs, a distributed optimization approach on the subregions of WSN like the one we are proposed allows to reduce the difficulty of a single global optimization problem by partitioning it in many smaller problems, one per subregion, that can be solved more easily. We have identified different research directions that arise out of the work presented here.
-We plan to extend our framework such that the schedules are planned for multiple
+We plan to extend our framework so that the schedules are planned for multiple
sensing periods.
%in order to compute all active sensor schedules in only one step for many periods;
We also want to improve our integer program to take into account heterogeneous
\section*{Acknowledgments}
-\noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully
+\noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully
acknowledge the University of Babylon - IRAQ for financial support and Campus
-France for the received support. This work has also been supported by the Labex
-ACTION.
+France for the received support. This work is also partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).
+
\ifCLASSOPTIONcaptionsoff
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